Question

Write the logic expression that matches the Truth Table below. A and C
are inputs, and Z is the output.
A
C Z
0
1 1
0
0 0
1
1 1
1
0
1

Answer 1

To write the logic expression that corresponds to the given truth table, we first need to interpret the data presented. Based on the information, we have an input A and an input C, and we need to determine when the output Z is 1.

### Truth Table Interpretation

We can represent the provided truth table more systematically. You'll need to identify when the output Z is 1:

| A | C | Z |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

From the above table, we see that Z outputs a '1' for the following combinations of inputs:

1. A = 0, C = 1 → \( A' C \)
2. A = 1, C = 0 → \( A C' \)
3. A = 1, C = 1 → \( A C \)

### Combining the Expressions

The logic expression that describes this behavior can be constructed by combining these minterms:

- \( A' C \) (for A = 0, C = 1)
- \( A C' \) (for A = 1, C = 0)
- \( A C \) (for A = 1, C = 1)

Thus, we can construct the overall expression for Z:

\[
Z = A' C + A C' + A C
\]

### Simplifying the Expression

You can further see that the expression \( A C' + A C \) can be simplified using the Consensus theorem:

\[
A(C' + C) = A
\]

So, the simplified expression becomes:

\[
Z = A' C + A
\]

This final expression means that Z is true when either A is true or when A is false and C is true.

### Final Logic Expression

Thus, the logic expression that matches the given truth table is:

\[
Z = A + A' C
\]

This can also be expressed in another equivalent form for completeness, if needed. However, \( Z = A + A' C \) is the simplest and correct representation based on the truth table provided.